The ratio of frequencies of two pendulum are 2:3, then their lengths are in ratio

Question

The ratio of frequencies of two pendulum are 2:3, then their lengths are in ratio, 2 / 3, 3 / 2, 4 / 9, 9 / 4

MARKS App · Accepted Answer

The time period ( T ) of a simple pendulum length l , is given by T = 2 π l g = 1 f r e q u e n c y ( n ) where g is acceleration due to gravity. ∴ n 1 n 2 = l 2 l 1 ⇒ l 1 l 2 = n 2 n 1 2 Given, n 2 n 1 = 3 2 ∴ l 1 l 2 = 3 2 2 = 9 4

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